Equivalent Ratios

Learn about equivalent ratios to get the
clear concept on ratio. We know that we use ratios to compare numbers.

How do we find two equivalent
ratios by using multiplication and division?

To get a ratio equivalent to a given
ratio we multiply or divide both the terms of the given ratio by the same
non-zero number. We will learn how to find the equivalent ratios of a given
ratio by writing the ratio as a fraction and then compare by using multiplication
and division.

Solved examples to find two
equivalent ratios:

1.
Give two equivalent ratios of 8 : 18.

Solution:

We will find the first equivalent ratio
of 8 : 18 by using multiplication.

So, first we need to write the given
ratio as fraction,

= 8/18

= (8 × 2)/(18 × 2)

= 16/36

= 16 : 36 (one equivalent ratio),

So, 16 : 36 is an equivalent ratio of 8 :
18.

Now we will find another equivalent ratio
of 8 : 18 by using division.

Similarly, first we need to write the
given ratio as fraction,

= 8/18

= (8 ÷ 2)/(18 ÷ 2)

= 4/9

= 4 : 9 (another equivalent ratio)

So, 4 : 9 is an equivalent ratio of 8 :
18.

Therefore, the two equivalent ratios of 8
: 18 are 16 : 36 and 4 : 9.

2.
Frame two equivalent ratios of 4 : 5.

Solution:

To findtwo equivalent ratios of 4 : 5 we need to apply multiplication
method only to get the answer in integer form.

First we need to write the given ratio as
fraction,

= 4/5

= (4 × 2)/(5 × 2)

= 8/10

= 8 : 10 is one equivalent ratio,

Similarly again, we need to write the
given ratio 4 : 5 as fraction to get another equivalent ratio;

= 4/5

= (4 × 3)/(5 × 3)

= 12/15 is another equivalent ratio

Therefore, the two equivalent ratios of 4
: 5 are 8 : 10 and 12 : 15.

Note: In this question we can’t apply division
method to get the answer in integer form because the G.C.F. of 4 and 5 is 1.
That means, 4 and 5 cannot be divisible by any other number except 1.

3.
For the following ratio find the two equivalent ratios of 11 : 13.

Solution:

To findtwo equivalent ratios of 11 : 13 first we need to write the given
ratio as fraction,